lesson 9.2 angle relationships and parallel lines

Lesson 9.2 Angle Relationships and Parallel Lines.

Anglesthat measure less than 90.

Angles that measure more than 90and less than 180.

Anglesthat measure exactly 90.

Types of Angles

Acute -

Right -

Obtuse -

Adjacent Angles

• Share a vertex and a side but no points in the interiors.

A

X

B

C

<AXB and <BXC are adjacent

angles

<AXC and <BXC are not adjacent angles

Why?

Complementary Angles

ab

- Angles whosesum is 90 .

m a m b 90

x y

m x m y 90

Complementary angles do nothave to be adjacent.

Supplementary Angles

kt

- Angles whosesum is 180 .

m k m t 180

b c

m b m c 180

Supplementary angles do nothave to be adjacent.

Congruent Angles

• Angles that have the same measurement• Notation:

1 3

1 3m m

Vertical Angles - Opposite angles that are formed by intersecting lines.

Opposite angles (vertical angles) are ALWAYS congruent.

b

a

ba

Identifying Corresponding Angles Transversal -A line that intersects

two other lines.

Identifying Corresponding Angles CorrespondingAngles

- Two angles that are formed by two lines and a transversal and occupy corresponding positions.

A B

C D

1 23 4

5 67 8

If the two lines are parallel, then the corresponding angles are congruent.

Corresponding Angles1 52 63 74 8

Identifying Alternate Interior Angles Alternate Interior Angles:-interior of a pair of lines on opposite

sides of the transversal.A B

C D

1 23 4

5 67 8

If the two lines are parallel, then the alternate interior angles are congruent.

Corresponding Angles3 64 5

(4n 30)

Find the value of n.

(n 10) (2n 30)

n

1) 2)

n (2n 30) 90 3n 30 90

30 30 3n 603 3n 20

(4n 30) (n 10) 180 5n 20 180

20 20 5n 1605 5n 32

Homework

• Page 452 -453 (1-11 all and 13)• Draw figures in the homework